The Mandelbrot set and the fractal nature of light, the Universe, and everything. L. Gardi lgardi@robarts.ca ABSTRACT “There is always another way to say the same thing that doesn’t look at all like the way it was said before.” Richard Feynman. In this essay, a novel approach to cosmology is presented that mathematically models the Universe as an iterated function system (IFS) analogous to the famous Mandelbrot Set IFS (M): z=z 2 +c, where z and c are complex numbers. In theoretical physics, wavefunctions are functions of a complex space that are commonly used to model the dynamics of particles and waves. In the IFS framework presented herein, complex dynamical systems are generated via the iteration process, where the act of iteration corresponds to 1) a change in the state of the system and 2) a change to the wavefunction itself. In this manner, M can be considered a wavefunction generator. In this framework, all observables, including gravity and time, are thought to be generated by the iteration process. Feynman understood that there are many ways of looking at the Universe that are equivalent in nature but different psychologically. Understanding cosmology in terms of fractals and iterated function systems requires a paradigm shift in the way we approach cosmology. This is an evidence based dissertation and does not contradict the standard model; rather, it attempts to reconstruct it using the principles of the fractal paradigm as outlined in this essay. It is the contention of the author that in order to understand the true nature of light, the universe and everything, we must first understand the important role that fractal cosmology plays in the study of our complex dynamical universe. Keywords: fractal, iteration, Mandelbrot set, wavefunction, black hole, event horizon, white hole, time, gravity, photon. PRELUDE This essay presents a scientific framework; that can be applied to the whole of the universe; that avoids some of the historical paradoxes; that answers some of the previously unanswered questions; and offers a new understanding of the nature of light, the universe and everything. This approach to cosmology has philosophical implications which are addressed throughout this essay. 1. INTRODUCTION The concept of fractals is relatively new in the field of mathematics, developed and popularized by the late Benoit Mandelbrot (1924 - 2010). Mandelbrot coined the term fractal to mean any fragmented structure with (theoretically) infinite complexity that has the property of self-similarity 1 . A more complete definition that captures essence the term fractal is as follows: Fractals are the emergent properties of iterative feedback systems, that exhibit both unpredictable and deterministic behaviours, forming patterns that manifest as complex coherent structures, with the property of scale invariance and self-similarity, displaying very specific boundary conditions, with complex morphologies that have a fractal dimension that uniquely quantifies the level of complexity of the emergent patterns within the system. This term fractal, however, was not in the minds of the founders of modern when they were developing the concepts that form the foundation of modern scientific thinking. Even Stephen Hawking admits that he does not know how to formulate physical laws on a fractal 2 since calculus, the main tool used by modern physics, does not work well on fractal manifolds. Understanding the universe in terms of fractal geometry requires a paradigm shift in the way we view the universe, which may require new laws and new tools. Although Hawking may concede that he does not know how to formulate physical The Nature of Light: What are Photons? V, edited by Chandrasekhar Roychoudhuri, Al F. Kracklauer, Hans De Raedt, Proc. of SPIE Vol. 8832, 883210 · © 2013 SPIE CCC code: 0277-786X/13/$18 · doi: 10.1117/12.2023739 Proc. of SPIE Vol. 8832 883210-1 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 10/15/2013 Terms of Use: http://spiedl.org/terms